The question of which topic areas should receive the greatest emphasis inschool mathematics is, I think, very much a function of culturalassumptions and biases. "Our" extended answer, as expressed in the U.S.National Council of Teachers of Mathematics' "Principles and standards forschool mathematics," is that five content and five process standards shouldpermeate the curriculum from kindergarten through grade 12. The contentstandards are:

Number and operations,*Algebra*GeometryMeasurement*Data analysis and probability.

I've starred the ones that are intended to receive the greatest emphasis atthe high school level. I should note that we do far less geometry than theChinese, even with this proposed emphasis; and that data analysis andprobability receive significant emphasis.

Here's a personal justification, based in American cultural assumptions.With the recognition that mathematics instruction can either be a "pump" ora "filter," either helping people advance or barring them from advancementin an increasingly technological society, we want as many people aspossible to have as many mathematical opportunities as possible. When Iwas a student, curricula were aimed for the mathematical elite; moststudents dropped out (50% each year from grade 9 on). Despite my Ph.D. inmathematics, my education was impoverished in some ways. I never had towrite coherent arguments (I just put numbers in a box at the end of mywork); I never made sense of real world phenomena using models or othermathematical tools; and I didn't study statistics until I taught it at thecollege level. Interestingly, those "defecits" in my own background arealso things that people who enter the workplace have strong needs for - wewant our citizens to be able to reason mathematically and convey theirreasoning effectiuvely orally and in prose, and to make sense of real-worldphenomena, using symolic modeling or statistical reasoning. Hence, acurriculum of the type suggested in "Principles and standards" could meetthe needs of citizens who intend to enter the workplace, and those who wishto pursue the study of mathematics. That's what's intended (I was writinggroup leader for the high school section.)

I imagine that with different cultural assumptions, one could justify acurriculum with different emphases. That's why I laid out mine in somedetail.